Properties

Label 260.1.be.a.67.1
Level $260$
Weight $1$
Character 260.67
Analytic conductor $0.130$
Analytic rank $0$
Dimension $4$
Projective image $D_{12}$
CM discriminant -4
Inner twists $4$

Related objects

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [260,1,Mod(63,260)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(260, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([6, 9, 7]))
 
N = Newforms(chi, 1, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("260.63");
 
S:= CuspForms(chi, 1);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 260 = 2^{2} \cdot 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 260.be (of order \(12\), degree \(4\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(0.129756903285\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\Q(\zeta_{12})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} - x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Projective image: \(D_{12}\)
Projective field: Galois closure of \(\mathbb{Q}[x]/(x^{12} - \cdots)\)

Embedding invariants

Embedding label 67.1
Root \(-0.866025 - 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 260.67
Dual form 260.1.be.a.163.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-0.866025 + 0.500000i) q^{5} -1.00000 q^{8} +(0.866025 + 0.500000i) q^{9} +O(q^{10})\) \(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-0.866025 + 0.500000i) q^{5} -1.00000 q^{8} +(0.866025 + 0.500000i) q^{9} +(-0.866025 - 0.500000i) q^{10} +(0.866025 - 0.500000i) q^{13} +(-0.500000 - 0.866025i) q^{16} +(-0.500000 - 1.86603i) q^{17} +1.00000i q^{18} -1.00000i q^{20} +(0.500000 - 0.866025i) q^{25} +(0.866025 + 0.500000i) q^{26} +(-0.866025 + 0.500000i) q^{29} +(0.500000 - 0.866025i) q^{32} +(1.36603 - 1.36603i) q^{34} +(-0.866025 + 0.500000i) q^{36} +(-1.50000 + 0.866025i) q^{37} +(0.866025 - 0.500000i) q^{40} +(0.500000 + 0.133975i) q^{41} -1.00000 q^{45} +(0.500000 + 0.866025i) q^{49} +1.00000 q^{50} +1.00000i q^{52} +(-0.366025 + 0.366025i) q^{53} +(-0.866025 - 0.500000i) q^{58} +(0.866025 - 1.50000i) q^{61} +1.00000 q^{64} +(-0.500000 + 0.866025i) q^{65} +(1.86603 + 0.500000i) q^{68} +(-0.866025 - 0.500000i) q^{72} -1.00000 q^{73} +(-1.50000 - 0.866025i) q^{74} +(0.866025 + 0.500000i) q^{80} +(0.500000 + 0.866025i) q^{81} +(0.133975 + 0.500000i) q^{82} +(1.36603 + 1.36603i) q^{85} +(-1.36603 - 0.366025i) q^{89} +(-0.500000 - 0.866025i) q^{90} +(-0.500000 + 0.866025i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 2 q^{2} - 2 q^{4} - 4 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + 2 q^{2} - 2 q^{4} - 4 q^{8} - 2 q^{16} - 2 q^{17} + 2 q^{25} + 2 q^{32} + 2 q^{34} - 6 q^{37} + 2 q^{41} - 4 q^{45} + 2 q^{49} + 4 q^{50} + 2 q^{53} + 4 q^{64} - 2 q^{65} + 4 q^{68} - 4 q^{73} - 6 q^{74} + 2 q^{81} + 4 q^{82} + 2 q^{85} - 2 q^{89} - 2 q^{90} - 2 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/260\mathbb{Z}\right)^\times\).

\(n\) \(41\) \(131\) \(157\)
\(\chi(n)\) \(e\left(\frac{1}{12}\right)\) \(-1\) \(e\left(\frac{1}{4}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(3\) 0 0 −0.965926 0.258819i \(-0.916667\pi\)
0.965926 + 0.258819i \(0.0833333\pi\)
\(4\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(5\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(6\) 0 0
\(7\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(8\) −1.00000 −1.00000
\(9\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(10\) −0.866025 0.500000i −0.866025 0.500000i
\(11\) 0 0 0.258819 0.965926i \(-0.416667\pi\)
−0.258819 + 0.965926i \(0.583333\pi\)
\(12\) 0 0
\(13\) 0.866025 0.500000i 0.866025 0.500000i
\(14\) 0 0
\(15\) 0 0
\(16\) −0.500000 0.866025i −0.500000 0.866025i
\(17\) −0.500000 1.86603i −0.500000 1.86603i −0.500000 0.866025i \(-0.666667\pi\)
1.00000i \(-0.5\pi\)
\(18\) 1.00000i 1.00000i
\(19\) 0 0 0.965926 0.258819i \(-0.0833333\pi\)
−0.965926 + 0.258819i \(0.916667\pi\)
\(20\) 1.00000i 1.00000i
\(21\) 0 0
\(22\) 0 0
\(23\) 0 0 0.258819 0.965926i \(-0.416667\pi\)
−0.258819 + 0.965926i \(0.583333\pi\)
\(24\) 0 0
\(25\) 0.500000 0.866025i 0.500000 0.866025i
\(26\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(27\) 0 0
\(28\) 0 0
\(29\) −0.866025 + 0.500000i −0.866025 + 0.500000i −0.866025 0.500000i \(-0.833333\pi\)
1.00000i \(0.5\pi\)
\(30\) 0 0
\(31\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(32\) 0.500000 0.866025i 0.500000 0.866025i
\(33\) 0 0
\(34\) 1.36603 1.36603i 1.36603 1.36603i
\(35\) 0 0
\(36\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(37\) −1.50000 + 0.866025i −1.50000 + 0.866025i −0.500000 + 0.866025i \(0.666667\pi\)
−1.00000 \(\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0.866025 0.500000i 0.866025 0.500000i
\(41\) 0.500000 + 0.133975i 0.500000 + 0.133975i 0.500000 0.866025i \(-0.333333\pi\)
1.00000i \(0.5\pi\)
\(42\) 0 0
\(43\) 0 0 0.965926 0.258819i \(-0.0833333\pi\)
−0.965926 + 0.258819i \(0.916667\pi\)
\(44\) 0 0
\(45\) −1.00000 −1.00000
\(46\) 0 0
\(47\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(48\) 0 0
\(49\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(50\) 1.00000 1.00000
\(51\) 0 0
\(52\) 1.00000i 1.00000i
\(53\) −0.366025 + 0.366025i −0.366025 + 0.366025i −0.866025 0.500000i \(-0.833333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 0 0
\(58\) −0.866025 0.500000i −0.866025 0.500000i
\(59\) 0 0 −0.258819 0.965926i \(-0.583333\pi\)
0.258819 + 0.965926i \(0.416667\pi\)
\(60\) 0 0
\(61\) 0.866025 1.50000i 0.866025 1.50000i 1.00000i \(-0.5\pi\)
0.866025 0.500000i \(-0.166667\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 1.00000 1.00000
\(65\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(66\) 0 0
\(67\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(68\) 1.86603 + 0.500000i 1.86603 + 0.500000i
\(69\) 0 0
\(70\) 0 0
\(71\) 0 0 −0.258819 0.965926i \(-0.583333\pi\)
0.258819 + 0.965926i \(0.416667\pi\)
\(72\) −0.866025 0.500000i −0.866025 0.500000i
\(73\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(74\) −1.50000 0.866025i −1.50000 0.866025i
\(75\) 0 0
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(80\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(81\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(82\) 0.133975 + 0.500000i 0.133975 + 0.500000i
\(83\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(84\) 0 0
\(85\) 1.36603 + 1.36603i 1.36603 + 1.36603i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −1.36603 0.366025i −1.36603 0.366025i −0.500000 0.866025i \(-0.666667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(90\) −0.500000 0.866025i −0.500000 0.866025i
\(91\) 0 0
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(98\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(99\) 0 0
\(100\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(101\) −1.50000 + 0.866025i −1.50000 + 0.866025i −0.500000 + 0.866025i \(0.666667\pi\)
−1.00000 \(\pi\)
\(102\) 0 0
\(103\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(104\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(105\) 0 0
\(106\) −0.500000 0.133975i −0.500000 0.133975i
\(107\) 0 0 0.258819 0.965926i \(-0.416667\pi\)
−0.258819 + 0.965926i \(0.583333\pi\)
\(108\) 0 0
\(109\) −1.00000 1.00000i −1.00000 1.00000i 1.00000i \(-0.5\pi\)
−1.00000 \(\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 0.133975 + 0.500000i 0.133975 + 0.500000i 1.00000 \(0\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 1.00000i 1.00000i
\(117\) 1.00000 1.00000
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) −0.866025 0.500000i −0.866025 0.500000i
\(122\) 1.73205 1.73205
\(123\) 0 0
\(124\) 0 0
\(125\) 1.00000i 1.00000i
\(126\) 0 0
\(127\) 0 0 −0.965926 0.258819i \(-0.916667\pi\)
0.965926 + 0.258819i \(0.0833333\pi\)
\(128\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(129\) 0 0
\(130\) −1.00000 −1.00000
\(131\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) 0 0
\(136\) 0.500000 + 1.86603i 0.500000 + 1.86603i
\(137\) 0.866025 + 0.500000i 0.866025 + 0.500000i 0.866025 0.500000i \(-0.166667\pi\)
1.00000i \(0.5\pi\)
\(138\) 0 0
\(139\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 0 0
\(144\) 1.00000i 1.00000i
\(145\) 0.500000 0.866025i 0.500000 0.866025i
\(146\) −0.500000 0.866025i −0.500000 0.866025i
\(147\) 0 0
\(148\) 1.73205i 1.73205i
\(149\) 1.86603 0.500000i 1.86603 0.500000i 0.866025 0.500000i \(-0.166667\pi\)
1.00000 \(0\)
\(150\) 0 0
\(151\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(152\) 0 0
\(153\) 0.500000 1.86603i 0.500000 1.86603i
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) −0.366025 0.366025i −0.366025 0.366025i 0.500000 0.866025i \(-0.333333\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 1.00000i 1.00000i
\(161\) 0 0
\(162\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(163\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(164\) −0.366025 + 0.366025i −0.366025 + 0.366025i
\(165\) 0 0
\(166\) 0 0
\(167\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(168\) 0 0
\(169\) 0.500000 0.866025i 0.500000 0.866025i
\(170\) −0.500000 + 1.86603i −0.500000 + 1.86603i
\(171\) 0 0
\(172\) 0 0
\(173\) 1.36603 0.366025i 1.36603 0.366025i 0.500000 0.866025i \(-0.333333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 0 0
\(178\) −0.366025 1.36603i −0.366025 1.36603i
\(179\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(180\) 0.500000 0.866025i 0.500000 0.866025i
\(181\) 1.00000i 1.00000i 0.866025 + 0.500000i \(0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 0.866025 1.50000i 0.866025 1.50000i
\(186\) 0 0
\(187\) 0 0
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(192\) 0 0
\(193\) 0.866025 + 1.50000i 0.866025 + 1.50000i 0.866025 + 0.500000i \(0.166667\pi\)
1.00000i \(0.5\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) −1.00000 −1.00000
\(197\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(198\) 0 0
\(199\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(200\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(201\) 0 0
\(202\) −1.50000 0.866025i −1.50000 0.866025i
\(203\) 0 0
\(204\) 0 0
\(205\) −0.500000 + 0.133975i −0.500000 + 0.133975i
\(206\) 0 0
\(207\) 0 0
\(208\) −0.866025 0.500000i −0.866025 0.500000i
\(209\) 0 0
\(210\) 0 0
\(211\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(212\) −0.133975 0.500000i −0.133975 0.500000i
\(213\) 0 0
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 0 0
\(218\) 0.366025 1.36603i 0.366025 1.36603i
\(219\) 0 0
\(220\) 0 0
\(221\) −1.36603 1.36603i −1.36603 1.36603i
\(222\) 0 0
\(223\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(224\) 0 0
\(225\) 0.866025 0.500000i 0.866025 0.500000i
\(226\) −0.366025 + 0.366025i −0.366025 + 0.366025i
\(227\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(228\) 0 0
\(229\) 1.00000 1.00000i 1.00000 1.00000i 1.00000i \(-0.5\pi\)
1.00000 \(0\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0.866025 0.500000i 0.866025 0.500000i
\(233\) −1.00000 1.00000i −1.00000 1.00000i 1.00000i \(-0.5\pi\)
−1.00000 \(\pi\)
\(234\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(235\) 0 0
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(240\) 0 0
\(241\) −1.86603 + 0.500000i −1.86603 + 0.500000i −0.866025 + 0.500000i \(0.833333\pi\)
−1.00000 \(1.00000\pi\)
\(242\) 1.00000i 1.00000i
\(243\) 0 0
\(244\) 0.866025 + 1.50000i 0.866025 + 1.50000i
\(245\) −0.866025 0.500000i −0.866025 0.500000i
\(246\) 0 0
\(247\) 0 0
\(248\) 0 0
\(249\) 0 0
\(250\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(251\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 0 0
\(255\) 0 0
\(256\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(257\) 1.86603 + 0.500000i 1.86603 + 0.500000i 1.00000 \(0\)
0.866025 + 0.500000i \(0.166667\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) −0.500000 0.866025i −0.500000 0.866025i
\(261\) −1.00000 −1.00000
\(262\) 0 0
\(263\) 0 0 −0.965926 0.258819i \(-0.916667\pi\)
0.965926 + 0.258819i \(0.0833333\pi\)
\(264\) 0 0
\(265\) 0.133975 0.500000i 0.133975 0.500000i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(270\) 0 0
\(271\) 0 0 0.258819 0.965926i \(-0.416667\pi\)
−0.258819 + 0.965926i \(0.583333\pi\)
\(272\) −1.36603 + 1.36603i −1.36603 + 1.36603i
\(273\) 0 0
\(274\) 1.00000i 1.00000i
\(275\) 0 0
\(276\) 0 0
\(277\) 0.500000 + 1.86603i 0.500000 + 1.86603i 0.500000 + 0.866025i \(0.333333\pi\)
1.00000i \(0.5\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 1.36603 + 1.36603i 1.36603 + 1.36603i 0.866025 + 0.500000i \(0.166667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(282\) 0 0
\(283\) 0 0 0.258819 0.965926i \(-0.416667\pi\)
−0.258819 + 0.965926i \(0.583333\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) 0.866025 0.500000i 0.866025 0.500000i
\(289\) −2.36603 + 1.36603i −2.36603 + 1.36603i
\(290\) 1.00000 1.00000
\(291\) 0 0
\(292\) 0.500000 0.866025i 0.500000 0.866025i
\(293\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(294\) 0 0
\(295\) 0 0
\(296\) 1.50000 0.866025i 1.50000 0.866025i
\(297\) 0 0
\(298\) 1.36603 + 1.36603i 1.36603 + 1.36603i
\(299\) 0 0
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 1.73205i 1.73205i
\(306\) 1.86603 0.500000i 1.86603 0.500000i
\(307\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(312\) 0 0
\(313\) −1.00000 + 1.00000i −1.00000 + 1.00000i 1.00000i \(0.5\pi\)
−1.00000 \(\pi\)
\(314\) 0.133975 0.500000i 0.133975 0.500000i
\(315\) 0 0
\(316\) 0 0
\(317\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(321\) 0 0
\(322\) 0 0
\(323\) 0 0
\(324\) −1.00000 −1.00000
\(325\) 1.00000i 1.00000i
\(326\) 0 0
\(327\) 0 0
\(328\) −0.500000 0.133975i −0.500000 0.133975i
\(329\) 0 0
\(330\) 0 0
\(331\) 0 0 −0.258819 0.965926i \(-0.583333\pi\)
0.258819 + 0.965926i \(0.416667\pi\)
\(332\) 0 0
\(333\) −1.73205 −1.73205
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) −0.366025 + 0.366025i −0.366025 + 0.366025i −0.866025 0.500000i \(-0.833333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(338\) 1.00000 1.00000
\(339\) 0 0
\(340\) −1.86603 + 0.500000i −1.86603 + 0.500000i
\(341\) 0 0
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) 0 0
\(346\) 1.00000 + 1.00000i 1.00000 + 1.00000i
\(347\) 0 0 0.965926 0.258819i \(-0.0833333\pi\)
−0.965926 + 0.258819i \(0.916667\pi\)
\(348\) 0 0
\(349\) 1.36603 + 0.366025i 1.36603 + 0.366025i 0.866025 0.500000i \(-0.166667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −1.50000 + 0.866025i −1.50000 + 0.866025i −0.500000 + 0.866025i \(0.666667\pi\)
−1.00000 \(\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 1.00000 1.00000i 1.00000 1.00000i
\(357\) 0 0
\(358\) 0 0
\(359\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(360\) 1.00000 1.00000
\(361\) 0.866025 0.500000i 0.866025 0.500000i
\(362\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(363\) 0 0
\(364\) 0 0
\(365\) 0.866025 0.500000i 0.866025 0.500000i
\(366\) 0 0
\(367\) 0 0 0.258819 0.965926i \(-0.416667\pi\)
−0.258819 + 0.965926i \(0.583333\pi\)
\(368\) 0 0
\(369\) 0.366025 + 0.366025i 0.366025 + 0.366025i
\(370\) 1.73205 1.73205
\(371\) 0 0
\(372\) 0 0
\(373\) 0.500000 + 1.86603i 0.500000 + 1.86603i 0.500000 + 0.866025i \(0.333333\pi\)
1.00000i \(0.5\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(378\) 0 0
\(379\) 0 0 0.258819 0.965926i \(-0.416667\pi\)
−0.258819 + 0.965926i \(0.583333\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) −0.866025 + 1.50000i −0.866025 + 1.50000i
\(387\) 0 0
\(388\) 0 0
\(389\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) −0.500000 0.866025i −0.500000 0.866025i
\(393\) 0 0
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) −1.00000 −1.00000
\(401\) 0.500000 1.86603i 0.500000 1.86603i 1.00000i \(-0.5\pi\)
0.500000 0.866025i \(-0.333333\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 1.73205i 1.73205i
\(405\) −0.866025 0.500000i −0.866025 0.500000i
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) −0.500000 + 0.133975i −0.500000 + 0.133975i −0.500000 0.866025i \(-0.666667\pi\)
1.00000i \(0.5\pi\)
\(410\) −0.366025 0.366025i −0.366025 0.366025i
\(411\) 0 0
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) 0 0
\(416\) 1.00000i 1.00000i
\(417\) 0 0
\(418\) 0 0
\(419\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(420\) 0 0
\(421\) 0.366025 0.366025i 0.366025 0.366025i −0.500000 0.866025i \(-0.666667\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0.366025 0.366025i 0.366025 0.366025i
\(425\) −1.86603 0.500000i −1.86603 0.500000i
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 0 0 −0.965926 0.258819i \(-0.916667\pi\)
0.965926 + 0.258819i \(0.0833333\pi\)
\(432\) 0 0
\(433\) −1.86603 + 0.500000i −1.86603 + 0.500000i −0.866025 + 0.500000i \(0.833333\pi\)
−1.00000 \(1.00000\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 1.36603 0.366025i 1.36603 0.366025i
\(437\) 0 0
\(438\) 0 0
\(439\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(440\) 0 0
\(441\) 1.00000i 1.00000i
\(442\) 0.500000 1.86603i 0.500000 1.86603i
\(443\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(444\) 0 0
\(445\) 1.36603 0.366025i 1.36603 0.366025i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −0.366025 1.36603i −0.366025 1.36603i −0.866025 0.500000i \(-0.833333\pi\)
0.500000 0.866025i \(-0.333333\pi\)
\(450\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(451\) 0 0
\(452\) −0.500000 0.133975i −0.500000 0.133975i
\(453\) 0 0
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −0.866025 1.50000i −0.866025 1.50000i −0.866025 0.500000i \(-0.833333\pi\)
1.00000i \(-0.5\pi\)
\(458\) 1.36603 + 0.366025i 1.36603 + 0.366025i
\(459\) 0 0
\(460\) 0 0
\(461\) −0.500000 1.86603i −0.500000 1.86603i −0.500000 0.866025i \(-0.666667\pi\)
1.00000i \(-0.5\pi\)
\(462\) 0 0
\(463\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(464\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(465\) 0 0
\(466\) 0.366025 1.36603i 0.366025 1.36603i
\(467\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(468\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(469\) 0 0
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 0 0
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) −0.500000 + 0.133975i −0.500000 + 0.133975i
\(478\) 0 0
\(479\) 0 0 −0.965926 0.258819i \(-0.916667\pi\)
0.965926 + 0.258819i \(0.0833333\pi\)
\(480\) 0 0
\(481\) −0.866025 + 1.50000i −0.866025 + 1.50000i
\(482\) −1.36603 1.36603i −1.36603 1.36603i
\(483\) 0 0
\(484\) 0.866025 0.500000i 0.866025 0.500000i
\(485\) 0 0
\(486\) 0 0
\(487\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(488\) −0.866025 + 1.50000i −0.866025 + 1.50000i
\(489\) 0 0
\(490\) 1.00000i 1.00000i
\(491\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(492\) 0 0
\(493\) 1.36603 + 1.36603i 1.36603 + 1.36603i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(500\) −0.866025 0.500000i −0.866025 0.500000i
\(501\) 0 0
\(502\) 0 0
\(503\) 0 0 −0.258819 0.965926i \(-0.583333\pi\)
0.258819 + 0.965926i \(0.416667\pi\)
\(504\) 0 0
\(505\) 0.866025 1.50000i 0.866025 1.50000i
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −0.133975 + 0.500000i −0.133975 + 0.500000i 0.866025 + 0.500000i \(0.166667\pi\)
−1.00000 \(\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) −1.00000 −1.00000
\(513\) 0 0
\(514\) 0.500000 + 1.86603i 0.500000 + 1.86603i
\(515\) 0 0
\(516\) 0 0
\(517\) 0 0
\(518\) 0 0
\(519\) 0 0
\(520\) 0.500000 0.866025i 0.500000 0.866025i
\(521\) 1.73205 1.73205 0.866025 0.500000i \(-0.166667\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(522\) −0.500000 0.866025i −0.500000 0.866025i
\(523\) 0 0 −0.965926 0.258819i \(-0.916667\pi\)
0.965926 + 0.258819i \(0.0833333\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 0 0
\(528\) 0 0
\(529\) −0.866025 0.500000i −0.866025 0.500000i
\(530\) 0.500000 0.133975i 0.500000 0.133975i
\(531\) 0 0
\(532\) 0 0
\(533\) 0.500000 0.133975i 0.500000 0.133975i
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) −0.366025 0.366025i −0.366025 0.366025i 0.500000 0.866025i \(-0.333333\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) −1.86603 0.500000i −1.86603 0.500000i
\(545\) 1.36603 + 0.366025i 1.36603 + 0.366025i
\(546\) 0 0
\(547\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(548\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(549\) 1.50000 0.866025i 1.50000 0.866025i
\(550\) 0 0
\(551\) 0 0
\(552\) 0 0
\(553\) 0 0
\(554\) −1.36603 + 1.36603i −1.36603 + 1.36603i
\(555\) 0 0
\(556\) 0 0
\(557\) 1.50000 0.866025i 1.50000 0.866025i 0.500000 0.866025i \(-0.333333\pi\)
1.00000 \(0\)
\(558\) 0 0
\(559\) 0 0
\(560\) 0 0
\(561\) 0 0
\(562\) −0.500000 + 1.86603i −0.500000 + 1.86603i
\(563\) 0 0 0.965926 0.258819i \(-0.0833333\pi\)
−0.965926 + 0.258819i \(0.916667\pi\)
\(564\) 0 0
\(565\) −0.366025 0.366025i −0.366025 0.366025i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(570\) 0 0
\(571\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 0 0
\(576\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(577\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(578\) −2.36603 1.36603i −2.36603 1.36603i
\(579\) 0 0
\(580\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(581\) 0 0
\(582\) 0 0
\(583\) 0 0
\(584\) 1.00000 1.00000
\(585\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(586\) 1.00000 1.00000
\(587\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(588\) 0 0
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) 1.50000 + 0.866025i 1.50000 + 0.866025i
\(593\) 1.73205 1.73205 0.866025 0.500000i \(-0.166667\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) −0.500000 + 1.86603i −0.500000 + 1.86603i
\(597\) 0 0
\(598\) 0 0
\(599\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(600\) 0 0
\(601\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 1.00000 1.00000
\(606\) 0 0
\(607\) 0 0 0.965926 0.258819i \(-0.0833333\pi\)
−0.965926 + 0.258819i \(0.916667\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) −1.50000 + 0.866025i −1.50000 + 0.866025i
\(611\) 0 0
\(612\) 1.36603 + 1.36603i 1.36603 + 1.36603i
\(613\) 0.866025 0.500000i 0.866025 0.500000i 1.00000i \(-0.5\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −0.866025 + 1.50000i −0.866025 + 1.50000i 1.00000i \(0.5\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(618\) 0 0
\(619\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) −0.500000 0.866025i −0.500000 0.866025i
\(626\) −1.36603 0.366025i −1.36603 0.366025i
\(627\) 0 0
\(628\) 0.500000 0.133975i 0.500000 0.133975i
\(629\) 2.36603 + 2.36603i 2.36603 + 2.36603i
\(630\) 0 0
\(631\) 0 0 0.965926 0.258819i \(-0.0833333\pi\)
−0.965926 + 0.258819i \(0.916667\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(635\) 0 0
\(636\) 0 0
\(637\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(638\) 0 0
\(639\) 0 0
\(640\) −0.866025 0.500000i −0.866025 0.500000i
\(641\) 1.50000 + 0.866025i 1.50000 + 0.866025i 1.00000 \(0\)
0.500000 + 0.866025i \(0.333333\pi\)
\(642\) 0 0
\(643\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 0 0 −0.965926 0.258819i \(-0.916667\pi\)
0.965926 + 0.258819i \(0.0833333\pi\)
\(648\) −0.500000 0.866025i −0.500000 0.866025i
\(649\) 0 0
\(650\) 0.866025 0.500000i 0.866025 0.500000i
\(651\) 0 0
\(652\) 0 0
\(653\) −1.36603 0.366025i −1.36603 0.366025i −0.500000 0.866025i \(-0.666667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) −0.133975 0.500000i −0.133975 0.500000i
\(657\) −0.866025 0.500000i −0.866025 0.500000i
\(658\) 0 0
\(659\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(660\) 0 0
\(661\) 0.133975 0.500000i 0.133975 0.500000i −0.866025 0.500000i \(-0.833333\pi\)
1.00000 \(0\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) −0.866025 1.50000i −0.866025 1.50000i
\(667\) 0 0
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) 0.133975 0.500000i 0.133975 0.500000i −0.866025 0.500000i \(-0.833333\pi\)
1.00000 \(0\)
\(674\) −0.500000 0.133975i −0.500000 0.133975i
\(675\) 0 0
\(676\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(677\) −1.00000 1.00000i −1.00000 1.00000i 1.00000i \(-0.5\pi\)
−1.00000 \(\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) −1.36603 1.36603i −1.36603 1.36603i
\(681\) 0 0
\(682\) 0 0
\(683\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(684\) 0 0
\(685\) −1.00000 −1.00000
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −0.133975 + 0.500000i −0.133975 + 0.500000i
\(690\) 0 0
\(691\) 0 0 −0.965926 0.258819i \(-0.916667\pi\)
0.965926 + 0.258819i \(0.0833333\pi\)
\(692\) −0.366025 + 1.36603i −0.366025 + 1.36603i
\(693\) 0 0
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 1.00000i 1.00000i
\(698\) 0.366025 + 1.36603i 0.366025 + 1.36603i
\(699\) 0 0
\(700\) 0 0
\(701\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) 0 0
\(705\) 0 0
\(706\) −1.50000 0.866025i −1.50000 0.866025i
\(707\) 0 0
\(708\) 0 0
\(709\) −0.500000 1.86603i −0.500000 1.86603i −0.500000 0.866025i \(-0.666667\pi\)
1.00000i \(-0.5\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 1.36603 + 0.366025i 1.36603 + 0.366025i
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(720\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(721\) 0 0
\(722\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(723\) 0 0
\(724\) −0.866025 0.500000i −0.866025 0.500000i
\(725\) 1.00000i 1.00000i
\(726\) 0 0
\(727\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(728\) 0 0
\(729\) 1.00000i 1.00000i
\(730\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(731\) 0 0
\(732\) 0 0
\(733\) 1.00000i 1.00000i −0.866025 0.500000i \(-0.833333\pi\)
0.866025 0.500000i \(-0.166667\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 0 0
\(738\) −0.133975 + 0.500000i −0.133975 + 0.500000i
\(739\) 0 0 −0.965926 0.258819i \(-0.916667\pi\)
0.965926 + 0.258819i \(0.0833333\pi\)
\(740\) 0.866025 + 1.50000i 0.866025 + 1.50000i
\(741\) 0 0
\(742\) 0 0
\(743\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(744\) 0 0
\(745\) −1.36603 + 1.36603i −1.36603 + 1.36603i
\(746\) −1.36603 + 1.36603i −1.36603 + 1.36603i
\(747\) 0 0
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) −1.00000 −1.00000
\(755\) 0 0
\(756\) 0 0
\(757\) 0.366025 1.36603i 0.366025 1.36603i −0.500000 0.866025i \(-0.666667\pi\)
0.866025 0.500000i \(-0.166667\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −1.36603 + 0.366025i −1.36603 + 0.366025i −0.866025 0.500000i \(-0.833333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) 0.500000 + 1.86603i 0.500000 + 1.86603i
\(766\) 0 0
\(767\) 0 0
\(768\) 0 0
\(769\) −0.366025 + 1.36603i −0.366025 + 1.36603i 0.500000 + 0.866025i \(0.333333\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −1.73205 −1.73205
\(773\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 0 0
\(778\) −0.500000 0.866025i −0.500000 0.866025i
\(779\) 0 0
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 0 0
\(784\) 0.500000 0.866025i 0.500000 0.866025i
\(785\) 0.500000 + 0.133975i 0.500000 + 0.133975i
\(786\) 0 0
\(787\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) 1.73205i 1.73205i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 0.366025 + 1.36603i 0.366025 + 1.36603i 0.866025 + 0.500000i \(0.166667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) −0.500000 0.866025i −0.500000 0.866025i
\(801\) −1.00000 1.00000i −1.00000 1.00000i
\(802\) 1.86603 0.500000i 1.86603 0.500000i
\(803\) 0 0
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 0 0
\(808\) 1.50000 0.866025i 1.50000 0.866025i
\(809\) 0.866025 0.500000i 0.866025 0.500000i 1.00000i \(-0.5\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(810\) 1.00000i 1.00000i
\(811\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) 0 0
\(818\) −0.366025 0.366025i −0.366025 0.366025i
\(819\) 0 0
\(820\) 0.133975 0.500000i 0.133975 0.500000i
\(821\) 1.36603 + 0.366025i 1.36603 + 0.366025i 0.866025 0.500000i \(-0.166667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(822\) 0 0
\(823\) 0 0 0.965926 0.258819i \(-0.0833333\pi\)
−0.965926 + 0.258819i \(0.916667\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(828\) 0 0
\(829\) −0.866025 1.50000i −0.866025 1.50000i −0.866025 0.500000i \(-0.833333\pi\)
1.00000i \(-0.5\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0.866025 0.500000i 0.866025 0.500000i
\(833\) 1.36603 1.36603i 1.36603 1.36603i
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 0 0 −0.258819 0.965926i \(-0.583333\pi\)
0.258819 + 0.965926i \(0.416667\pi\)
\(840\) 0 0
\(841\) 0 0
\(842\) 0.500000 + 0.133975i 0.500000 + 0.133975i
\(843\) 0 0
\(844\) 0 0
\(845\) 1.00000i 1.00000i
\(846\) 0 0
\(847\) 0 0
\(848\) 0.500000 + 0.133975i 0.500000 + 0.133975i
\(849\) 0 0
\(850\) −0.500000 1.86603i −0.500000 1.86603i
\(851\) 0 0
\(852\) 0 0
\(853\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 0.366025 0.366025i 0.366025 0.366025i −0.500000 0.866025i \(-0.666667\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(858\) 0 0
\(859\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(864\) 0 0
\(865\) −1.00000 + 1.00000i −1.00000 + 1.00000i
\(866\) −1.36603 1.36603i −1.36603 1.36603i
\(867\) 0 0
\(868\) 0 0
\(869\) 0 0
\(870\) 0 0
\(871\) 0 0
\(872\) 1.00000 + 1.00000i 1.00000 + 1.00000i
\(873\) 0 0
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) 0.866025 1.50000i 0.866025 1.50000i 1.00000i \(-0.5\pi\)
0.866025 0.500000i \(-0.166667\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) −0.866025 + 0.500000i −0.866025 + 0.500000i −0.866025 0.500000i \(-0.833333\pi\)
1.00000i \(0.5\pi\)
\(882\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(883\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(884\) 1.86603 0.500000i 1.86603 0.500000i
\(885\) 0 0
\(886\) 0 0
\(887\) 0 0 0.258819 0.965926i \(-0.416667\pi\)
−0.258819 + 0.965926i \(0.583333\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 1.00000 + 1.00000i 1.00000 + 1.00000i
\(891\) 0 0
\(892\) 0 0
\(893\) 0 0
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) 0 0
\(898\) 1.00000 1.00000i 1.00000 1.00000i
\(899\) 0 0
\(900\) 1.00000i 1.00000i
\(901\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(902\) 0 0
\(903\) 0 0
\(904\) −0.133975 0.500000i −0.133975 0.500000i
\(905\) −0.500000 0.866025i −0.500000 0.866025i
\(906\) 0 0
\(907\) 0 0 −0.965926 0.258819i \(-0.916667\pi\)
0.965926 + 0.258819i \(0.0833333\pi\)
\(908\) 0 0
\(909\) −1.73205 −1.73205
\(910\) 0 0
\(911\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(912\) 0 0
\(913\) 0 0
\(914\) 0.866025 1.50000i 0.866025 1.50000i
\(915\) 0 0
\(916\) 0.366025 + 1.36603i 0.366025 + 1.36603i
\(917\) 0 0
\(918\) 0 0
\(919\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 1.36603 1.36603i 1.36603 1.36603i
\(923\) 0 0
\(924\) 0 0
\(925\) 1.73205i 1.73205i
\(926\) 0 0
\(927\) 0 0
\(928\) 1.00000i 1.00000i
\(929\) 0.500000 0.133975i 0.500000 0.133975i 1.00000i \(-0.5\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 1.36603 0.366025i 1.36603 0.366025i
\(933\) 0 0
\(934\) 0 0
\(935\) 0 0
\(936\) −1.00000 −1.00000
\(937\) 0.366025 + 0.366025i 0.366025 + 0.366025i 0.866025 0.500000i \(-0.166667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) −1.00000 + 1.00000i −1.00000 + 1.00000i 1.00000i \(0.5\pi\)
−1.00000 \(\pi\)
\(942\) 0 0
\(943\) 0 0
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(948\) 0 0
\(949\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) −1.36603 + 0.366025i −1.36603 + 0.366025i −0.866025 0.500000i \(-0.833333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(954\) −0.366025 0.366025i −0.366025 0.366025i
\(955\) 0 0
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 0 0
\(960\) 0 0
\(961\) 1.00000i 1.00000i
\(962\) −1.73205 −1.73205
\(963\) 0 0
\(964\) 0.500000 1.86603i 0.500000 1.86603i
\(965\) −1.50000 0.866025i −1.50000 0.866025i
\(966\) 0 0
\(967\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(968\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(969\) 0 0
\(970\) 0 0
\(971\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) 0 0
\(975\) 0 0
\(976\) −1.73205 −1.73205
\(977\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(978\) 0 0
\(979\) 0 0
\(980\) 0.866025 0.500000i 0.866025 0.500000i
\(981\) −0.366025 1.36603i −0.366025 1.36603i
\(982\) 0 0
\(983\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) −0.500000 + 1.86603i −0.500000 + 1.86603i
\(987\) 0 0
\(988\) 0 0
\(989\) 0 0
\(990\) 0 0
\(991\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) −1.86603 + 0.500000i −1.86603 + 0.500000i −0.866025 + 0.500000i \(0.833333\pi\)
−1.00000 \(1.00000\pi\)
\(998\) 0 0
\(999\) 0 0
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 260.1.be.a.67.1 4
3.2 odd 2 2340.1.em.a.847.1 4
4.3 odd 2 CM 260.1.be.a.67.1 4
5.2 odd 4 1300.1.bt.a.743.1 4
5.3 odd 4 260.1.bl.a.223.1 yes 4
5.4 even 2 1300.1.bm.a.1107.1 4
12.11 even 2 2340.1.em.a.847.1 4
13.2 odd 12 3380.1.l.c.2127.2 4
13.3 even 3 3380.1.s.b.2267.1 4
13.4 even 6 3380.1.be.c.2047.1 4
13.5 odd 4 3380.1.bl.d.427.1 4
13.6 odd 12 3380.1.bl.c.2347.1 4
13.7 odd 12 260.1.bl.a.7.1 yes 4
13.8 odd 4 3380.1.bl.b.427.1 4
13.9 even 3 3380.1.be.e.2047.1 4
13.10 even 6 3380.1.s.c.2267.2 4
13.11 odd 12 3380.1.l.b.2127.1 4
13.12 even 2 3380.1.be.b.587.1 4
15.8 even 4 2340.1.hj.c.1783.1 4
20.3 even 4 260.1.bl.a.223.1 yes 4
20.7 even 4 1300.1.bt.a.743.1 4
20.19 odd 2 1300.1.bm.a.1107.1 4
39.20 even 12 2340.1.hj.c.1567.1 4
52.3 odd 6 3380.1.s.b.2267.1 4
52.7 even 12 260.1.bl.a.7.1 yes 4
52.11 even 12 3380.1.l.b.2127.1 4
52.15 even 12 3380.1.l.c.2127.2 4
52.19 even 12 3380.1.bl.c.2347.1 4
52.23 odd 6 3380.1.s.c.2267.2 4
52.31 even 4 3380.1.bl.d.427.1 4
52.35 odd 6 3380.1.be.e.2047.1 4
52.43 odd 6 3380.1.be.c.2047.1 4
52.47 even 4 3380.1.bl.b.427.1 4
52.51 odd 2 3380.1.be.b.587.1 4
60.23 odd 4 2340.1.hj.c.1783.1 4
65.3 odd 12 3380.1.l.b.2943.2 4
65.7 even 12 1300.1.bm.a.943.1 4
65.8 even 4 3380.1.be.e.1103.1 4
65.18 even 4 3380.1.be.c.1103.1 4
65.23 odd 12 3380.1.l.c.2943.1 4
65.28 even 12 3380.1.s.c.2803.2 4
65.33 even 12 inner 260.1.be.a.163.1 yes 4
65.38 odd 4 3380.1.bl.c.1263.1 4
65.43 odd 12 3380.1.bl.d.2723.1 4
65.48 odd 12 3380.1.bl.b.2723.1 4
65.58 even 12 3380.1.be.b.3023.1 4
65.59 odd 12 1300.1.bt.a.7.1 4
65.63 even 12 3380.1.s.b.2803.1 4
156.59 odd 12 2340.1.hj.c.1567.1 4
195.98 odd 12 2340.1.em.a.163.1 4
260.3 even 12 3380.1.l.b.2943.2 4
260.7 odd 12 1300.1.bm.a.943.1 4
260.23 even 12 3380.1.l.c.2943.1 4
260.43 even 12 3380.1.bl.d.2723.1 4
260.59 even 12 1300.1.bt.a.7.1 4
260.63 odd 12 3380.1.s.b.2803.1 4
260.83 odd 4 3380.1.be.c.1103.1 4
260.103 even 4 3380.1.bl.c.1263.1 4
260.123 odd 12 3380.1.be.b.3023.1 4
260.163 odd 12 inner 260.1.be.a.163.1 yes 4
260.203 odd 4 3380.1.be.e.1103.1 4
260.223 odd 12 3380.1.s.c.2803.2 4
260.243 even 12 3380.1.bl.b.2723.1 4
780.683 even 12 2340.1.em.a.163.1 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
260.1.be.a.67.1 4 1.1 even 1 trivial
260.1.be.a.67.1 4 4.3 odd 2 CM
260.1.be.a.163.1 yes 4 65.33 even 12 inner
260.1.be.a.163.1 yes 4 260.163 odd 12 inner
260.1.bl.a.7.1 yes 4 13.7 odd 12
260.1.bl.a.7.1 yes 4 52.7 even 12
260.1.bl.a.223.1 yes 4 5.3 odd 4
260.1.bl.a.223.1 yes 4 20.3 even 4
1300.1.bm.a.943.1 4 65.7 even 12
1300.1.bm.a.943.1 4 260.7 odd 12
1300.1.bm.a.1107.1 4 5.4 even 2
1300.1.bm.a.1107.1 4 20.19 odd 2
1300.1.bt.a.7.1 4 65.59 odd 12
1300.1.bt.a.7.1 4 260.59 even 12
1300.1.bt.a.743.1 4 5.2 odd 4
1300.1.bt.a.743.1 4 20.7 even 4
2340.1.em.a.163.1 4 195.98 odd 12
2340.1.em.a.163.1 4 780.683 even 12
2340.1.em.a.847.1 4 3.2 odd 2
2340.1.em.a.847.1 4 12.11 even 2
2340.1.hj.c.1567.1 4 39.20 even 12
2340.1.hj.c.1567.1 4 156.59 odd 12
2340.1.hj.c.1783.1 4 15.8 even 4
2340.1.hj.c.1783.1 4 60.23 odd 4
3380.1.l.b.2127.1 4 13.11 odd 12
3380.1.l.b.2127.1 4 52.11 even 12
3380.1.l.b.2943.2 4 65.3 odd 12
3380.1.l.b.2943.2 4 260.3 even 12
3380.1.l.c.2127.2 4 13.2 odd 12
3380.1.l.c.2127.2 4 52.15 even 12
3380.1.l.c.2943.1 4 65.23 odd 12
3380.1.l.c.2943.1 4 260.23 even 12
3380.1.s.b.2267.1 4 13.3 even 3
3380.1.s.b.2267.1 4 52.3 odd 6
3380.1.s.b.2803.1 4 65.63 even 12
3380.1.s.b.2803.1 4 260.63 odd 12
3380.1.s.c.2267.2 4 13.10 even 6
3380.1.s.c.2267.2 4 52.23 odd 6
3380.1.s.c.2803.2 4 65.28 even 12
3380.1.s.c.2803.2 4 260.223 odd 12
3380.1.be.b.587.1 4 13.12 even 2
3380.1.be.b.587.1 4 52.51 odd 2
3380.1.be.b.3023.1 4 65.58 even 12
3380.1.be.b.3023.1 4 260.123 odd 12
3380.1.be.c.1103.1 4 65.18 even 4
3380.1.be.c.1103.1 4 260.83 odd 4
3380.1.be.c.2047.1 4 13.4 even 6
3380.1.be.c.2047.1 4 52.43 odd 6
3380.1.be.e.1103.1 4 65.8 even 4
3380.1.be.e.1103.1 4 260.203 odd 4
3380.1.be.e.2047.1 4 13.9 even 3
3380.1.be.e.2047.1 4 52.35 odd 6
3380.1.bl.b.427.1 4 13.8 odd 4
3380.1.bl.b.427.1 4 52.47 even 4
3380.1.bl.b.2723.1 4 65.48 odd 12
3380.1.bl.b.2723.1 4 260.243 even 12
3380.1.bl.c.1263.1 4 65.38 odd 4
3380.1.bl.c.1263.1 4 260.103 even 4
3380.1.bl.c.2347.1 4 13.6 odd 12
3380.1.bl.c.2347.1 4 52.19 even 12
3380.1.bl.d.427.1 4 13.5 odd 4
3380.1.bl.d.427.1 4 52.31 even 4
3380.1.bl.d.2723.1 4 65.43 odd 12
3380.1.bl.d.2723.1 4 260.43 even 12